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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Superposed hyperbolic kink and pulse solutions of coupled $φ$ 4 , NLS and mKdV equations

Here, in this paper, we obtain novel solutions of a coupled $φ$ 4 , a coupled nonlinear Schrödinger equation and a coupled modified Korteweg de Vries equation which can be re-expressed as a linear superposition of either the sum or the difference of two hyperbolic pulse solutions or the sum of either a two-kink or a kink and an antikink solution. These results demonstrate that the notion of superposed solutions extends to coupled nonlinear equations as well.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Linear model decision trees as surrogates in optimization of engineering applications

Machine learning models are promising as surrogates in optimization when replacing difficult to solve equations or black-box type models. This work demonstrates the viability of linear model decision trees as piecewise-linear surrogates in decision-making problems. Linear model decision trees can be represented exactly in mixed-integer linear programming (MILP) and mixed-integer quadratic constrained programming (MIQCP) formulations. Furthermore, they can represent discontinuous functions, bringing advantages over neural networks in some cases. We present several formulations using transformations from Generalized Disjunctive Programming (GDP) formulations and modifications of MILP formulations for gradient boosted decision trees (GBDT). We then compare the computational performance of these different MILP and MIQCP representations in an optimization problem and illustrate their use on engineering applications. Importantly, we observe faster solution times for optimization problems with linear model decision tree surrogates when compared with GBDT surrogates using the Optimization and Machine Learning Toolkit (OMLT).

42 ENGINEERING↗
DOE OSTI2021

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations

In this work, we present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\mathcal{O}(N\log^2 N)$ computation and $\mathcal{O}(N)$ memory complexity when applied to an $N\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Nonexistence of integrable nonlinear magnetic fields with invariants quadratic in momenta

Nonlinear, completely integrable Hamiltonian systems that serve as blueprints for novel particle accelerators at the intensity frontier are promising avenues for research, as Fermilab’s Integrable Optics Test Accelerator (IOTA) example clearly illustrates. Here, we show that only very limited generalizations are possible when no approximations in the underlying Hamiltonian or Maxwell equations are allowed, as was the case for IOTA. Specifically, no such systems exist with invariants quadratic in the momenta, precluding straightforward generalization of the Courant-Snyder theory of linear integrable systems in beam physics. We also conjecture that no such systems exist with invariants of higher degree in the momenta. This leaves solenoidal magnetic fields, including their nonlinear fringe fields, as the only completely integrable static magnetic fields, albeit with invariants that are linear in the momenta. The difficulties come from enforcing Maxwell equations; without constraints, we show that there are many solutions. In particular, we discover a previously unknown large family of integrable Hamiltonians.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Two-epoch Orbit Estimation for Wide Binaries Resolved in Hipparcos and Gaia

The Hipparcos catalog and its Double and Multiple System Annex (DMSA) lists 4099 components with individual proper motions and coordinates on the epoch 1991.25. Many of these long-period binary stars are also present in Gaia Data Release 2 (DR2). Using the available relative positions and proper motions separated by 24.25 yr, the equations of relative orbital motion can be solved for the two epoch eccentric anomalies, orbital period, and eccentricity. This method employs elimination of the linear Thiele–Innes unknowns and nonlinear optimization of the remaining condition equations. The quality of these solutions is compromised by the insufficient condition and modest precision of the Hipparcos astrometric data, as revealed by Monte Carlo simulations with artificially perturbed data points. The presence of multiple systems and optical pairs can also perturb the results. Limited experiments with artificial data indicate that useful estimates can be obtained with a 25 yr epoch difference for wide binaries with orbital periods up to ~500 yr. The prospects of this method dramatically improve with the proposed next-generation space astrometry missions such as Gaia-NIR and Theia, especially when additional conditions are included from astrometric or spectroscopic measurements. An ancillary catalog of cross-identification and astrometric information for 1295 double-star pairs cross-matched in Gaia DR2 and Hipparcos is also published.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Error Estimates for the Optimal Control of a Parabolic Fractional PDE

In this work, we consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates for the optimal variables. To discretize the state equation we propose a fully discrete scheme that relies on an implicit finite difference discretization in time combined with a piecewise linear finite element discretization in space. We derive stability results and a novel $L^2(0,T;L^2(\Omega))$ a priori error estimate. On the basis of the aforementioned solution technique, we propose a fully discrete scheme for our optimal control problem that discretizes the control variable with piecewise constant functions, and we derive a priori error estimates for it. We illustrate the theory with one- and two-dimensional numerical experiments.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Generalized Kompaneets formalism for inelastic neutrino-nucleon scattering in supernova simulations

Based on the Kompaneets approximation, we develop a robust methodology to calculate spectral redistribution via inelastic neutrino-nucleon scattering in the context of core-collapse supernova simulations. The resulting equations conserve lepton number to machine precision and scale linearly, not quadratically, with number of energy groups. The formalism also provides an elegant means to derive the rate of energy transfer to matter which, as it must, automatically goes to zero when the neutrino radiation field is in thermal equilibrium. Furthermore, we derive the next higher order in $ϵ/mc^2$ correction to the neutrino Kompaneets equation. Unlike other Kompaneets schema, ours also generalizes to the case of anisotropic angular distributions, while retaining the conservative form that is a hallmark of the classical Kompaneets equation. In this work, our formalism enables immediate incorporation into supernova codes that follow the spectral angular moments of the neutrino radiation fields.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Second-Order Invariant Domain Preserving ALE Approximation of Euler Equations

Abstract An invariant domain preserving arbitrary Lagrangian-Eulerian method for solving non-linear hyperbolic systems is developed. The numerical scheme is explicit in time and the approximation in space is done with continuous finite elements. The method is made invariant domain preserving for the Euler equations using convex limiting and is tested on various benchmarks.

Guermond, Jean-Luc↗
DOE OSTI2023

Hierarchical Model Reduction Driven by Machine Learning for Parametric Advection-Diffusion-Reaction Problems in the Presence of Noisy Data

Abstract We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model reduction with a standard Proper Orthogonal Decomposition, according to an offline/online paradigm. In this paper we show that directional HiPOD looses in terms of accuracy when problem data are affected by noise. This is due to the interpolation driving the online phase, since it replicates, by definition, the noise trend. To overcome this limit, we replace interpolation with Machine Learning fitting models which better discriminate relevant physical features in the data from irrelevant unstructured noise. The numerical assessment, although preliminary, confirms the potentialities of the new approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Benchmark of numerical modeling approaches on the systematic performance evaluation of wave energy converters

Different numerical modeling methods have been developed and applied to evaluate a variety of performance indicators of wave energy converters (WECs), including the power performance, structural loads, levelized cost of energy, etc. Based on the modeling fidelity, the commonly used numerical modeling approaches can be classified as linear modeling, weakly nonlinear modeling and fully nonlinear modeling approaches. Each method differs in accuracy and computational efficiency, making them suitable for different stages of WEC design. However, the selection of modeling approach could significantly impact evaluation outcomes. For instance, simplified linear models may underestimate structural loads or overestimate energy production in some operational conditions, potentially leading to less cost-effective designs. Given the widespread utilization of these models, it is essential to understand the uncertainties brought by them in performance evaluations. This work is dedicated to benchmarking different linear-potential-flow-based numerical models for evaluating the systematic performance of WECs. Three representative numerical modeling approaches are considered in this work, including linear frequency-domain modeling, statistically linearized spectral-domain modeling and Cummins equation-based nonlinear time-domain modeling. A generic point absorber WEC is considered as the research reference in this work, and different sea sites are taken into account. The numerical models are utilized to predict critical performance indicators, including power performance, the annual energy production, the capacity factor, the levelized cost of energy and the PTO fatigue loads. By comparing the results, this work identifies the uncertainties associated with different modeling approaches in evaluating WEC performance.

Fatigue↗
DOE OSTI2026

Fast solvers for tokamak fluid models with PETSc

Multigrid (MG) is widely recognized as a highly effective solver for the model problem, the Laplacian, but textbook MG fails on most problems of interest. MG methods have been applied to complex, real-world applications with careful consideration of the physical model and discretization. In this work we develop the first step in applying MG methods to science and engineering relevant magnetohydrodynamics (MHD) tokamak models in the M3D-C1 (https://m3dc1.pppl.gov) fusion energy science code. The semi-implicit time integrator in M3D-C1 is composed of many linear solves. The implicit advance of the momentum equation is the most challenging and is the focus of this work. The current production solver in M3D-C1 is a block Jacobi (BJ) preconditioner within a Krylov solver, where blocks group degrees of freedom on planes of constant toroidal coordinate. BJ convergence degrades as the number of planes increases due to the spectral properties of the matrix preconditioned with BJ. The partially magnetic field-aligned, regular toroidal grid structure in M3D-C1 is amenable to semi-coarsening geometric MG in the toroidal direction. This paper develops such a solver and demonstrates competitive performance on a runaway electron model of a SPARC (https://cfs.energy/technology/sparc) disruption, and superior robustness on a stellarator model on which the BJ solver fails to converge.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Nonlinear dynamics of multiple Alfvén modes driven by trapped energetic ions in tokamaks: A triplet paradigm

Non-linear dynamics of multiple infernal Alfvén eigenmodes—a subset of global Alfvén eigenmodes in tokamak plasmas with extended low-shear central core [Marchenko et al., Phys. Plasmas 16, 092502 (2009)]—is studied. The analysis is carried out for a mode triplet with toroidal mode-numbers n=1, 2, 3. It was assumed that the n = 1 mode was linearly unstable due to precession resonance with trapped fast ions, whereas the other modes were linearly damped. The modes were coupled due to a non-linearity in a bounce-averaged drift kinetic equation for the distribution function of fast ions. Nonlinear equations for the mode amplitudes and phases are derived and solved numerically. It is found that the temporal evolution of the amplitudes and the phase (responsible for the frequency chirping) of the modes exhibit Hopf bifurcations to stable limit cycles. This can explain a synchronous cyclic destabilization of multiple modes in Alfvén avalanches (sudden growth of amplitudes of the mode cluster with different n and approximately equal frequency spacing) in NSTX and bursting modes in MAST—events, which resulted in enhanced loss of fast ions.

Marchenko, V. S. (ORCID:0000000261480533)↗
DOE OSTI2023

Using the Stix finite element RF code to investigate operation optimization of the ICRF antenna on Alcator C-Mod

Abstract As the Ion Cyclotron Radio Frequency range (ICRF) heating becomes more favorable in fusion devices, the urgency of predicting and mitigating impurity generation that arises from it becomes more pressing. In the ICRF regime, rectified Radio Frequency (RF) sheaths are known to form at antenna and material edges that influence negative effects like sputtering and a decrease in heating efficiency. Methods to mitigate the formation of these RF sheaths through RF image currents cancellation have been experimentally studied. A power-phasing scan done on Alcator C-Mod in which the amount of power on the two inner straps ( P in ) versus the total 4 straps ( P tot ) was varied showed a minimization of enhanced potentials between P in / P tot ∼ 0.7–0.9 while impurities were minimized for P in / P tot ∼ 0.5–0.8. New capabilities in the realm of representing the RF sheath numerically now allow for these experiments to be simulated. Given the size of the sheath relative to the scale of the device, it can be approximated as a Boundary Condition (BC). A new parallelized cold-plasma wave equation solver called Stix implements a non-linear sheath impedance model BC formulated by Myra et al (2015 Phys. Plasmas 22 062507) through the method of finite elements using the MFEM library [ http://mfem.org ]. It is seen that Stix shows qualitative agreement with the measured C-Mod enhanced potentials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Resilient Operating Constraints for Power Distribution Systems under Setpoint Attacks

Integration and operation of distributed generation (DG) and energy storage (ES) in power distribution systems are enabled by communication networks and embedded sensor and control devices that increase the vulnerability of the systems to cyber-threats, broadening the attack surface and making adversary actions more unpredictable. This paper proposes a methodology that uses ellipsoidal approximations to quantify the potential damage caused by successful attacks that affect, directly or indirectly, the desired operation setpoints and may drive the power distribution operation to unsafe states by violating the limits of voltage or line flows. More specifically, a new methodology is introduced to find the optimal non-symmetric operating constraints that can be imposed to each DG and ES in order to guarantee that the power distribution system is resilient to any malicious setpoints. The proposed method takes as inputs the system topology, DG and ES capabilities, and load limits to solve a convex optimization problem formulated using linear matrix inequalities (LMIs) and the power flow equations. The proposed solution is agnostic to the attacker's action or load profile and it does not require any assumption about the location or means of the attack. The numerical results on a test distribution feeder with several DG and ES illustrate how the proposed resilient operating constraints guarantee the security of the power distribution system under setpoint attacks.

Giraldo, Jairo↗
DOE OSTI2026

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Dynamical chemistry: non-equilibrium effective actions for reactive fluids

Abstract We present two approaches for describing chemical reactions taking place in fluid phase. The first method mirrors the usual derivation of the hydrodynamic equations of motion by relating conserved—or to account for chemical reactions, non-conserved—currents to local-equilibrium parameters. The second method involves a higher-brow approach in which we attack the same problem from the perspective of non-equilibrium effective field theory (EFT). Non-equilibrium effective actions are defined using the in–in formalism on the Schwinger–Keldysh contour and are therefore capable of describing thermal fluctuations and dissipation as well as quantum effects. The non-equilibrium EFT approach is especially powerful as all terms in the action are fully specified by the symmetries of the system; in particular the second law of thermodynamics does not need to be included by hand, but is instead derived from the action itself. We find that the equations of motion generated by both methods agree, but the EFT approach yields certain advantages. To demonstrate some of these advantages we construct a quadratic action that is valid to very small distance scales—much smaller than the scales at which ordinary hydrodynamic theories break down. Such an action captures the full thermodynamic and quantum behavior of reactions and diffusion at quadratic order. Finally, taking the low-frequency and low-wavenumber limit, we reproduce the linearized version of the well-known reaction–diffusion equations as a final coherence check.

Mechanics↗
DOE OSTI2026

Laplace Transform–Based Quantum Eigenvalue Transformation via Linear Combination of Hamiltonian Simulation

Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value transformations are well studied, eigenvalue transformations are distinct, especially for nonnormal matrices. Here, we propose an efficient quantum algorithm for performing a class of eigenvalue transformations that can be expressed as a certain type of matrix Laplace transformation. This allows us to significantly extend the recently developed linear combination of Hamiltonian simulation method [D. An, J.-P. Liu, and L. Lin, Phys. Rev. Lett., 131 (2023), 150603; D. An, A. M. Childs, and L. Lin, Commun. Math. Phys. 407, 19 (2026)] to represent a wider class of eigenvalue transformations, such as powers of the matrix inverse, 𝐴 −𝑘 , and the exponential of the matrix inverse, 𝑒 −𝐴 −1 . The latter can be interpreted as the solution of a mass-matrix differential equation of the form form 𝐴⁢𝑢′⁡⁡(𝑡) =−𝑢⁡(𝑡). We demonstrate that our eigenvalue transformation approach can solve this problem without explicitly inverting 𝐴, thereby reducing the computational complexity.

Laplace transform↗